To find David's relative error, we need to use the formula for relative error:
\[ \text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|} \]
In this case, the measured value is 8.9 and the actual value is 9. Let's plug these values into the formula.
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Calculate the absolute error: \[ |\text{Measured Value} - \text{Actual Value}| = |8.9 - 9| = |-0.1| = 0.1 \]
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Calculate the absolute value of the actual value: \[ |\text{Actual Value}| = |9| = 9 \]
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Now we can calculate the relative error: \[ \text{Relative Error} = \frac{0.1}{9} \]
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Perform the division: \[ \frac{0.1}{9} \approx 0.0111111 \]
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Finally, round to the nearest hundredth: \[ 0.0111111 \approx 0.01 \]
Therefore, David's relative error to the nearest hundredth is:
\[ \boxed{0.01} \]